#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
#define drep(i, cc, n) for (ll i = (cc); i <= (n); ++i)
#define rep(i, n) drep(i, 0, n - 1)
#define all(a) (a).begin(), (a).end()
#define pb push_back
#define fi first
#define se second
mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());
const ll MOD1000000007 = 1000000007;
const ll MOD998244353 = 998244353;
const ll MOD[3] = {999727999, 1070777777, 1000000007};
const ll LINF = 1LL << 60LL;
const int IINF = (1 << 30) - 1;


template<typename T>
struct edge{
    int from, to;
    T cost;
    int id;

    edge(){}
    edge(int to, T cost=1) : from(-1), to(to), cost(cost){}
    edge(int to, T cost, int id) : from(-1), to(to), cost(cost), id(id){}
    edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id){}
};

template<typename T>
struct redge{
    int from, to;
    T cap, cost;
    int rev;
    
    redge(int to, T cap, T cost=(T)(1)) : from(-1), to(to), cap(cap), cost(cost){}
    redge(int to, T cap, T cost, int rev) : from(-1), to(to), cap(cap), cost(cost), rev(rev){}
};

template<typename T> using Edges = vector<edge<T>>;
template<typename T> using weighted_graph = vector<Edges<T>>;
template<typename T> using tree = vector<Edges<T>>;
using unweighted_graph = vector<vector<int>>;
template<typename T> using residual_graph = vector<vector<redge<T>>>;


template<typename W>
struct lowest_common_ancestor{
    int root = 0;
    int n;
    int log_n = 1;
    vector<vector<int>> par;
    vector<int> depth;

    lowest_common_ancestor(tree<W> &T, int root=0) : root(root){
        n = (int)T.size();
        while((1 << log_n) < n) log_n++;
        par.resize(log_n, vector<int>(n, -1));
        depth.resize(n, 0);
        init(T);
    }

    void init(tree<W> &T){
        function<void(int, int)> dfs = [&](int v, int p){
            par[0][v] = p;
            for(edge<W> e : T[v]) if(e.to!=p){
                depth[e.to] = depth[v]+1;
                dfs(e.to, v);
            }
        };

        dfs(root, -1);
        for(int k=0; k+1<log_n; k++){
            for(int v=0; v<n; v++){
                if(par[k][v]<0) par[k+1][v] = -1;
                else par[k+1][v] = par[k][par[k][v]];
            }
        }
    }

    int query(int u, int v){
        if(depth[u] < depth[v]) swap(u, v);
        for(int k=0; k<log_n; k++) if((depth[u]-depth[v]) >> k & 1) u = par[k][u];

        if(u == v) return u;
        for(int k=log_n-1; k>=0; k--){
            if(par[k][u] != par[k][v]){
                u = par[k][u];
                v = par[k][v];
            }
        }

        return par[0][u];
    }
};


void solve(){
	int n; cin >> n;
	vector<int> a(n);
	for(int i=0; i<n; i++) cin >> a[i];
	{
		vector<int> c(n);
		for(int i=0; i<n; i++) c[i] = a[i];
		sort(all(c));
		c.erase(unique(all(c)), c.end());
		for(int i=0; i<n; i++) a[i] = lower_bound(all(c), a[i])-c.begin();
	}

	tree<int> T(n);
	for(int i=0; i<n-1; i++){
		int u, v; cin >> u >> v;
		u--; v--;
		T[u].pb(edge<int>(v));
		T[v].pb(edge<int>(u));
	}

	lowest_common_ancestor<int> lca(T);
	vector<int> depth(n, 0);
	function<void(int, int)> dfs = [&](int v, int p){
		for(edge<int> e : T[v]) if(e.to!=p){
			depth[e.to] = depth[v]+1;
			dfs(e.to, v);
		}
	}; dfs(0, -1);

	function<int(int, int)> dist = [&](int u, int v){
		return depth[u] + depth[v] -2*depth[lca.query(u, v)];
	};

	vector<vector<int>> b(n);
	for(int i=0; i<n; i++) b[a[i]].push_back(i);

	int s = -1, t = -1;
	int diam = 0;
	vector<int> ans(n, 0);
	for(int i=n-1; i>=0; i--){
		//追加
		for(int v : b[i]){
			if(s==-1){
				s = v;
				t = v;
				diam = 0;
			}else{
				int s_dist = dist(s, v);
				int t_dist = dist(t, v);
				if(diam < max(s_dist, t_dist)){
					if(s_dist>=t_dist){
						t = v;
						diam = s_dist;
					}else{
						s = v;
						diam = t_dist;
					}
				}
			}
		}

		for(int v : b[i]){
			ans[v] = max(dist(s, v), dist(t, v));
		}
	}

	for(int i=0; i<n; i++) cout << ans[i]  << " ";
	cout << '\n';
}

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	
	int T=1;
	//cin >> T;
	while(T--) solve();
}